If you rebarrel the 98 will handle almost any standard round. The list is almost endless. I am partial to the 260, 243, 250-3000, 257 Rob. or possibley the best choice of all the 7x57. Loaded to moderate velocity with a 140 grain bullet that's a bit soft(I like the Nosler Ballistic tip) it is a really great shooting and deadly round, with minimal recoil. The same can be said for the 280(Chose that one for my daughter). She killed 3 or 4 in a row, one shot each with hers(before that she used a 243 for 3-4). I use the same basic load concept, a soft 140 and moderate load. She can't hunt much the last few years, college keeps her busy,,I miss that time, terribly.
The Roberts is also a great round for a kid just starting. Kills good, accurate and light in the recoil department. As to the best way to go... I can't really lie to you. If you have to farm out the work, building custom rifles is costly. You can pick up a used commercially made rifle for less money and it'll work just fine. If you can do most of the work yourself and have the time, it can mean a special rifle for a you boy(or girl). Of course we'll be here to help anyway we can... Take a kid to the woods, teach them to hunt, it teaches them about life..